Just to expand on this:

"ye" in "ye Olde mill" is actually just "the" but originally "þe"/"þee". The first printing presses to England were imported from Germany, which never used þ, so printers used something that looked sorta similar, thus "y".

"Ye" was a different word, the 2nd person non-formal version of "you" (which was historically formal: see-Shakespeare and how he played with "ye" and "you"). Thorn was on its way out along with "ð" both of which were in Middle English. The sounds didn't leave English, but we merged it into one letter cluster "th" (think "that" and "the", which have different th sounds).